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1/59x+60)=2/3x-2
We move all terms to the left:
1/59x+60)-(2/3x-2)=0
Domain of the equation: 59x!=0
x!=0/59
x!=0
x∈R
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
1/59x+60)-(2/3x=0
We calculate fractions
3x/177x^2-(2*59x)/177x^2+60=0
We add all the numbers together, and all the variables
3x/177x^2-(+2*59x)/177x^2+60=0
We multiply all the terms by the denominator
3x-(+2*59x)+60*177x^2=0
Wy multiply elements
10620x^2+3x-(+2*59x)=0
We get rid of parentheses
10620x^2+3x-2*59x=0
Wy multiply elements
10620x^2+3x-118x=0
We add all the numbers together, and all the variables
10620x^2-115x=0
a = 10620; b = -115; c = 0;
Δ = b2-4ac
Δ = -1152-4·10620·0
Δ = 13225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{13225}=115$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-115)-115}{2*10620}=\frac{0}{21240} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-115)+115}{2*10620}=\frac{230}{21240} =23/2124 $
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